Sounds like that’s a good thing in case some wacko lib where to get in not that would happen in your state.
It could cut both ways but in Tx the Lt Gov is the one in charge, followed by the AG.
The executive branch consists of the Governor, Lieutenant Governor, Comptroller of Public Accounts, Land Commissioner, Attorney General, Agriculture Commissioner, the three-member Texas Railroad Commission, the State Board of Education, and the Secretary of State. Texas has a plural executive branch system which limits the power of the Governor. Except for the Secretary of State, all executive officers are elected independently making them directly answerable to the public, not the Governor.[2]
Partly because of many elected officials, the governor’s powers are quite limited in comparison to other state governors or the U.S. President. In popular lore and belief the lieutenant governor, who heads the Senate and appoints its committees, has more power than the governor. The governor commands the state militia and can veto bills passed by the Legislature and call special sessions of the Legislature (this power is exclusive to the governor and can be exercised as often as desired). The governor also appoints members of various executive boards and fills judicial vacancies between elections. All members of the executive branch are elected statewide except for the Secretary of State (appointed) and the State Board of Education (each of its 15 members are elected from single-member districts).